Absolute accuracy and sensitivity analysis of OP-FTIR ... · non-linear least squares ﬁtting...

Atmos. Meas. Tech., 4, 97–116, 2011www.atmos-meas-tech.net/4/97/2011/doi:10.5194/amt-4-97-2011© Author(s) 2011. CC Attribution 3.0 License.

AtmosphericMeasurement

Techniques

Absolute accuracy and sensitivity analysis of OP-FTIR retrievals ofCO2, CH4 and CO over concentrations representative of “clean air”and “polluted plumes”

T. E. L. Smith1, M. J. Wooster1,2, M. Tattaris 1, and D. W. T. Griffith 3

1King’s College London, Environmental Monitoring and Modelling Research Group, Department of Geography, Strand,London, WC2R 2LS, UK2NERC National Centre for Earth Observation, UK3University of Wollongong, Centre for Atmospheric Chemistry, Wollongong, NSW 2522, Australia

Received: 15 June 2010 – Published in Atmos. Meas. Tech. Discuss.: 23 August 2010Revised: 5 January 2011 – Accepted: 6 January 2011 – Published: 26 January 2011

Abstract. When compared to established point-samplingmethods, Open-Path Fourier Transform Infrared (OP-FTIR)spectroscopy can provide path-integrated concentrations ofmultiple gases simultaneously, in situ and near-continuously.The trace gas pathlength amounts can be retrieved from themeasured IR spectra using a forward model coupled to anon-linear least squares fitting procedure, without requiring“background” spectral measurements unaffected by the gasesof interest. However, few studies have investigated the accu-racy of such retrievals for CO2, CH4 and CO, particularlyacross broad concentration ranges covering those character-istic of ambient to highly polluted air (e.g. from biomassburning or industrial plumes). Here we perform such an as-sessment using data collected by a field-portable FTIR spec-trometer. The FTIR was positioned to view a fixed IR sourceplaced at the other end of an IR-transparent cell filled withthe gases of interest, whose target concentrations were var-ied by more than two orders of magnitude. Retrievals madeusing the model are complicated by absorption line pressurebroadening, the effects of temperature on absorption bandshape, and by convolution of the gas absorption lines and theinstrument line shape (ILS). Despite this, with careful modelparameterisation (i.e. the optimum wavenumber range, ILS,and assumed gas temperature and pressure for the retrieval),concentrations for all target gases were able to be retrievedto within 5%. Sensitivity to the aforementioned model in-puts was also investigated. CO retrievals were shown to be

Correspondence to:T. E. L. Smith([email protected])

most sensitive to the ILS (a function of the assumed instru-ment field-of-view), which is due to the narrow nature of COabsorption lines and their consequent sensitivity to convolu-tion with the ILS. Conversely, CO2 retrievals were most sen-sitive to assumed atmospheric parameters, particularly gastemperature. Our findings provide confidence that FTIR-derived trace gas retrievals of CO2, CH4 and CO based onmodeling can yield results with high accuracies, even oververy large (many order of magnitude) concentration rangesthat can prove difficult to retrieve via standard classical leastsquares (CLS) techniques. With the methods employed here,we suggest that errors in the retrieved trace gas concentra-tions should remain well below 10%, even with the uncer-tainties in atmospheric pressure and temperature that mightarise when studying plumes in more difficult field situations(e.g. at uncertain altitudes or temperatures).

1 Introduction

In many applications, remote sensing of gas species pres-ence and concentrations offer advantages over establishedpoint-sampling and/or laboratory analysis methods. Open-path (OP) Fourier Transform Infrared (FTIR) spectroscopycan be used to detect and quantify a wide range of gases si-multaneously; can operate in situ, eliminating contaminationfrom tubing or sample handling; can operate continuously,providing real-time data at a relatively high temporal reso-lution (seconds); and can be used over long path lengths,providing path-integrated gas concentrations less prone to

Published by Copernicus Publications on behalf of the European Geosciences Union.

http://creativecommons.org/licenses/by/3.0/

98 T. E. L. Smith et al.: Absolute accuracy and sensitivity analysis of OP-FTIR retrievals

artefacts induced by point-based sampling and which cannoteasily be acquired using alternative approaches.

A variety of analysis techniques are available to retrievetrace gas concentrations from measured single-beam spectraacquired by FTIR instrumentation. These generally involvecomparing the measured spectra with reference spectra ofthe gas of interest under known conditions of temperature,pressure and concentration. Reference spectra may comefrom laboratory measurements of gases, or may be syntheti-cally generated (e.g. Griffith, 1996) from molecular absorp-tion databases, such as HITRAN (Rothman et al., 2009). Oneretrieval technique involves converting the measured spectrainto absorbance units and fitting the reference spectra usingclassical least squares (CLS) or partial least squares meth-ods over a spectral window within which the trace gas ofinterest has significant features (Haaland, 1990). One diffi-culty with this approach can be the necessity to obtain “back-ground” single beam spectra unaffected by the gases of in-terest, these being combined with the single-beam observa-tions of interest to derive the values of absorbance (Bacsiket al., 2004). Alternatively, the single-beam reference spec-tra may be modelled and iteratively fitted to the measuredspectra using nonlinear least squares (NLLS) (e.g. Griffithet al., 2003). The accuracy of both methods is generallygauged via a goodness-of-fit measure between the measuredand modelled/reference spectra. However, only a few pub-lished studies have determined absolute retrieval accuraciesvia independent accuracy assessments based on experimen-tal methods using cells containing known gas concentrations(see Esler et al., 2000; Horrocks et al., 2001). This is sur-prising given the sensitivity of retrieval methods to anal-ysis parameters such as spectral window position and ex-tent, gas temperature and pressure, and instrument line shape(Hart et al., 1999; Horrocks et al., 2001). OP-FTIR spec-troscopy is being used increasingly as a method for moni-toring key carbonaceous greenhouse and tracer species suchas CO2, CH4 and CO. Given that OP-FTIR spectroscopyof these and other trace gas species is being applied in anever-increasing range of applications, including volcanology(Horrocks et al., 1999; Oppenheimer et al., 2002); urban andaircraft pollution assessment (Grutter, 2003; Grutter et al.,2003; Hong et al., 2004; Schafer et al., 1995, 2003) agri-cultural emission estimation (Childers et al., 2001; Griffithet al., 2002); and biomass burning investigations (Griffith etal., 1991; Yokelson et al., 1997), it is important that the trueaccuracy of the method is established over the wide range ofpotential concentrations found in these applications. Here weuse an experimentally-based laboratory setup to determinethe absolute accuracy of OP-FTIR retrievals of carbon diox-ide (CO2), carbon monoxide (CO) and methane (CH4) madeusing the modelling approach across a concentration rangeencompassing both ambient air and highly polluted plumes(such as those emanating from vegetation fires, vehicle pol-lution or biogenic sources).

2 Background

In some cases, the accuracy of FTIR retrievals has beeninferred via comparisons of the retrieved concentrations tothose from more established point-sampling techniques, suchas nondispersive infrared (NDIR) spectroscopy for CO2 andCO (e.g. Gerlach et al., 1998), or gas chromatography (GC)(e.g. Goode et al., 1999) or wet chemistry (e.g. von Bobrutzkiet al., 2010) for other gases. For laboratory biomass burning,Goode et al. (1999) compared FTIR concentration retrievalsmade using synthetic reference spectra and CLS analysis,with those from GC. CO2 retrievals from FTIR were shownto agree to within 1% of the GC results, although FTIR re-trievals of CO and CH4 were shown to generally underesti-mate concentrations by∼6% when compared with GC. Ger-lach et al. (1998) compared CO2/SO2 ratios derived fromFTIR, NDIR and GC, finding general agreement betweenall three methods. Whilst these results are encouraging interms of the apparent agreement between FTIR and alter-native approaches, they only represent intercomparisons be-tween methods essentially employing rather different sam-pling strategies.

To achieve a true absolute accuracy assessment for FTIRretrievals, it is necessary to measure the IR spectra of wellcharacterised, laboratory prepared, calibrated gas mixturesand compare the gas concentrations retrieved from thesemeasurements to the known true concentrations. Only a lim-ited number of studies have undertaken such a procedure(e.g. Horrocks et al., 2001; Esler et al., 2000; Lamp et al.,1997). Esler et al. (2000) were primarily interested in deter-mining the precision of FTIR gas analysis of CO2, CH4, COand N2O, using a sample of clean air (Southern Hemisphere“baseline” air) introduced into a 9.8 m White cell, analysingthe measured spectra using a CLS approach and syntheticallygenerated absorbance spectra. For CO2, the method provedto be highly accurate giving a retrieval accuracy of 0.006%compared to GC analysis of the same sample, and for CH4,CO and N2O, 0.03%, 1.0% and 0.1% respectively. These ex-cellent accuracy statistics for ambient air unfortunately werenot extended to measurements covering a broader range ofconcentrations. Optimal retrievals made at higher concentra-tions (and equivalently longer pathlengths, since the methodactually responds to the number of gas molecules present inthe optical path) might require use of different parameter-isatons of the forward model (for example the spectral win-dow). This maybe due, for example, to absorption saturationor deviations from the standard Beer-Lambert law causedby deviations in absorptivity coefficients at high concentra-tions due to interactions between molecules in close proxim-ity (Zhu and Griffiths, 1998).

Lamp et al. (1997) generated gas mixtures using mass flowcontrollers to yield a broad concentration range of CH4 (8–1900 ppmm) and CO (10–3120 ppmm – parts per millionmeters) in a 20 m White cell. CLS analysis of the result-ing IR absorbance spectra showed a significant nonlinear

Atmos. Meas. Tech., 4, 97–116, 2011 www.atmos-meas-tech.net/4/97/2011/

T. E. L. Smith et al.: Absolute accuracy and sensitivity analysis of OP-FTIR retrievals 99

relationship between measured and known concentrations.For CH4, retrieved values were within 5% of the true con-centrations below 700 ppmm, but accuracy halved at higherconcentrations. Lamp et al. (1997) demonstrated that useof strong absorption regions, such as the CH4 Q-branch at3017 cm−1, can lead to reduced accuracy as concentrationincreases, and a switch to other spectral windows might bemore appropriate. CO retrievals were shown to suffer fromsimilar nonlinearities, with concentration underestimated bymore than 50% at concentrations higher than 1000 ppmm.

An alternative to CLS-based methods is to use a nonlinearleast squares (NLLS) fitting procedure (Marquardt, 1963).This approach can fit single-beam spectra directly and re-quires no assumption of Beer-Lambert linearity, allowing forthe use of both weak and strong absorption regions (Griffithet al., 2003). In a comparison between retrievals made usingCLS and NLLS methods, Childers et al. (2002) found that forCO2, CH4, NH3 and N2O, the CLS method generally under-estimated at higher gas concentrations. To demonstrate thiseffect, Fig. 1 illustrates retrievals made here using the CLSand NLLS approach from spectra of a gas cell containingCO2 gas of varying concentrations, topped up with nitrogento maintain ambient pressure (the experimental method is de-scribed fully in Sect. 3 of this paper). The underestimationof high CO2 concentrations when using the CLS method isclearly evident, and is due to the aforementioned nonlineardeviation from the Beer-Lambert law.

For volcanological applications, Horrocks et al. (2001)used a similar experimental setup and spectral modelling ap-proach to that employed here to test the accuracy of OP-FTIRretrievals of SO2 over a wide range of absorber amounts(125 ppmm–10 500 ppmm). As is the case here, insteadof using a White cell to increase pathlength, Horrocks etal. (2001) chose to use higher mixing ratios (ppm) of SO2,which are equivalent to a longer path according to the Beer-Lambert law:

τ = α Lc (1)

where optical depth (τ , unitless) is equal to the product of theabsorption coefficient of the sample (α, [ppmm]−1), the pathlength of the sample (L, m) and the mixing ratio of the sam-ple (c, ppm). Optical depth is related to the true transmission(T , unitless) following Eq. (2):

T = e−τ (2)

The measured transmittance is the true transmittance con-volved with the instrument line shape (ILS). Horrocks etal. (2001) found that increased retrieval accuracies wereachieved as concentrations of SO2 increased, improving from∼5.6% at 125 ppmm to within 1.0% at 10 500 ppmm. Thisstudy builds on this work by using a similar approach to es-tablish the OP-FTIR retrieval accuracies for CO2, CO andCH4 at mixing ratios ranging from those found in ambientair to those found in polluted cities, biomass burning smoke

Fig. 1. Comparison of FTIR-derived retrievals of gas-cell CO2pathlength amount to the true pathlength amount within the cell.Retrievals were made from the same spectra via two approaches,the Classical Least Squares (CLS) approach described in Haa-land (1990) and the MALT forward model and nonlinear leastsquares (NLLS) fitting procedure described in Griffith (1996) andGriffith et al. (2003). The 1:1 line is shown, and the increasingunderestimation of the CLS-based retrievals at higher pathlengthamounts is clearly evident.

and volcanic plumes, a much broader range than investigatedby Esler et al. (2000). We follow Horrocks et al. (2001)and analyse the collected IR spectra using an iterative NLLSmethod coupled to a forward modelling approach, specif-ically the Multi-Atmospheric Layer Transmission (MALT)model described in Griffith (1996) and Griffith et al. (2003).The work of Lamp et al. (1997) showed how Beer-Lambertlaw divergence can impact retrieval accuracy when investi-gating high concentration gases using spectral regions con-taining strong IR absorbance features. Generating retrievalsfrom modelled synthetic spectra fitted to the measured spec-tra in the way conducted here should avoid these problemsand the associated concentration underestimation illustratedin the CLS-derived results displayed Fig. 1.

3 Instrumentation and setup

Our study utilised facilities of the UK’s Natural Environ-ment Research Council’s Molecular Spectroscopy Facility,part of the Rutherford Appleton Laboratory. A stainless steelgas cell of circular cross section was fitted with IR transpar-ent KBr windows at each end and was filled with the sam-ple gas at the concentration of interest before each spectralmeasurement. Gas cell length was 1.05 m, diameter 160 mmand IR window diameter 135 mm. The spectrometer used

www.atmos-meas-tech.net/4/97/2011/ Atmos. Meas. Tech., 4, 97–116, 2011


Table 1. Cell mixing ratios (ppm) and equivalent pathlength amounts (ppmm) for the 1.05 m gas cell filled with CO2, CH4 and CO respec-tively, with the equivalent mixing ratios for longer atmospheric paths (assuming the same temperature,∼20◦C, and pressure,∼1000 hPaconditions) also given. For reference, ambient “clean” air mixing ratios of CO2, CH4 and CO are circa 385 ppm, 1.8 ppm and 0.15 ppm,respectively.

Cell mixing Cell Pathlength Equivalent Equivalent Equivalentratio amount mixing ratio for mixing ratio for mixing ratio for

(ppm) (ppmm) a 30 m path a 100 m path a 800 m path(ppm) (ppm) (ppm)

CO2

12 014 12 612 420.4 126.1 15.824 991 26 236 874.5 262.4 32.845 799 48 080 1602.7 480.8 60.1

100 125 105 112 3503.7 1051.1 131.4200 200 210 172 7005.7 2101.7 262.7340 351 357 304 11910.1 3573.0 446.6

CH4

51.94 54.52 1.83 0.55 0.0792.81 97.43 3.25 0.97 0.12

168.51 176.91 5.90 1.77 0.22270.85 284.34 9.48 2.84 0.36490.09 514.50 17.15 5.15 0.64

CO

18.96 19.90 0.66 0.20 0.03244.14 256.30 8.54 2.56 0.32459.13 482.00 16.07 4.82 0.60

1217.05 1277.67 42.59 12.78 1.606077.20 6379.91 212.66 63.80 7.98

Fig. 2. Schematic of the physical instrumentation arrangement used in the current study.

was a MIDAC Corporation FTIR Air Monitoring system, fit-ted with a mercury cadmium telluride (MCT) detector andZnSe optics. The spectrometer was optically coupled to a76 mm Newtonian telescope and placed to view an IR sourcethrough the IR transparent windows of the gas cell. TheIR source used was a SiC globar operating at 1100 K, po-sitioned at the focus of a 150 mm collimator. This setup,

shown in Fig. 2, is very similar to that used by Horrocks etal. (2001), with a total pathlength of∼1.5 m, 0.5 m of whichconsisted of free air between the cell and spectrometer andcell and IR source, together with air inside the spectrome-ter housing. The CO2 and H2O mixing ratios in the ambi-ent airoutside of the cellwere monitored using a calibratedLICOR 840 NDIR gas analyser. An attenuator was fitted to



the FTIR spectrometer telescope to avoid MCT detector sat-uration, and the temperature of the gas inside the gas cellmeasured using a platinum resistance thermometer (PRT).

Table 1 lists the gas mixtures investigated. As describedby the Beer-Lambert law (Eq. 1), it is possible to simulate alonger OP measurement pathlength by increasing the mixingratio of the gas sample inside the cell, since pathlength (L)and mixing ratio (c) equivalently increase the number of gasmolecules in the open path over which the IR spectra are ac-quired. However, for target gas mixing ratios above∼1% (inair or N2) the linewidths will become significantly affectedby self broadening relative to longer path-lower concentra-tion spectra of the same total pathlength amount. This affectseach of the CO2 mixtures used in this study, but not the othergases since their mixing ratios are significantly lower. TheMALT model includes a mixing ratio-weighted linewidth toaccount for this self broadening effect.

The mixing ratios used here were chosen to represent arange covering those from clean air measured over short-to-long pathlengths in the natural environment (e.g. 10–1000 m), as well as polluted air across the same pathlengthrange, and range up to mixing ratios that might be foundin pollutant plumes (e.g. from industrial sources or biomassburning). For example, six different CO2 pathlength-concentration products (hereafter called pathlength amount)were used, spanning∼12 500 ppmm to∼360 000 ppmm. Ifthese pathlength amounts are expressed as mixing ratios us-ing pathlengths typically employed in the field, both the low-est and highest cell mixing ratios yield a CO2 mixing ratioof ∼420–450 ppm for a 30 m and 800 m path respectively,equivalent to typical ambient CO2 conditions found in urbansettings (e.g. Rigby et al., 2008).

Gas mixtures were prepared manometrically using highpurity (99.9%) component gases. The mixing method re-lied on three MKS Baratron (type 690) pressure capacitancemanometers operated at three precision levels of 0.1 Pa, 10 Paand 100 Pa with a stated accuracy of±0.05%. The manome-ters were also used to test the sealing of the gas cell, record-ing a <1% change in cell pressure over 18 h when filled toambient pressure (1000 hPa). For each gas concentration tobe studied, the cell was evacuated before the sample gas(CO2, CO or CH4) was slowly released into the cell untilthe desired mixing ratio was reached. After waiting for thepressure to stabilise and noting the final pressure, the cellwas filled with nitrogen to ambient pressure (1000 hPa) andallowed to stabilise once more. After stabilisation, 10 IRspectrum were measured with the FTIR spectrometer, eachconsisting of 8 co-added scans (a total of∼9 s scan timeper spectra) in order to increase signal-to-noise. The rela-tive standard deviations among each set of 10 replicate sin-gle beam spectral measurements ranged from 0.1–1.2%, withstandard errors of the means of 0.03–0.4% for these measure-ment conditions. The partial pressure of the sample gas wasused to calculate the true sample mixing ratio (ppm) by divid-ing the partial pressure of the sample gas by the final ambient

pressure of the gas cell. To avoid contamination by gas fromthe previous mixture, the lowest concentration of each gaswas mixed first, working up to higher concentrations.

4 Procedure for gas concentration retrieval

4.1 Spectrum simulation and fitting algorithm

Spectra were analysed using a NLLS method combined witha forward modelling approach, whereby NLLS was used tofit a modelled spectrum to a measured spectrum, thus solvingthe inverse problem of returning gas concentrations from theobservations. The method is quite commonly applied in OP-FTIR studies, and examples include SFIT2 (Rinsland et al.,1998), often used to retrieve total atmospheric column tracegas abundances (e.g. Hase et al., 2006; Fu et al., 2007 andSenten et al., 2008), but also used for ground-based open-path studies (e.g. Briz et al., 2007). A similar procedure (Bur-ton et al., 1998) has been commonly applied to the retrievalof gas concentrations from open path measurements of vol-canic plumes (e.g. Oppenheimer et al., 1998; Horrocks et al.,1999 and Richter et al., 2002). The specific retrieval pro-cedure used here is based on the Multi-Atmospheric LayerTransmission (MALT) model of Griffith (1996) and Griffithet al. (2003), whose past applications include the analysis ofopen-path, White cell, and solar occultation spectra (Goodeet al., 1999; Goode et al., 2000; Bertschi et al., 2003; Galleet al., 2000; Griffith et al., 2002).

The background theory to the inverse problem is detailedin Rodgers (2000). By denoting the measurement spectrumas vectory (the measurement vector) and the variables to beretrieved (the trace gas concentrations) as the state vectorx,the measurement and its relation to the state vector, can bedescribed as:

y = f (x) (3)

wheref (x) is the forward function, describing the physicsof the measurement. It is unlikely that the physics of a sys-tem will be known and understood with full accuracy. HenceEq. (3) is adapted as:

y = F(x) + ε (4)

F(x), the forward model, approximates the physics of themeasurement, andε is the measurement error. HereF(x)

represents the simulated single beam spectrum.The radiative transfer forward model used to simulate the

spectraF(x) is detailed in Griffith (1996). To parameterisethe calculation ofF(x) for each measured single-beam spec-trum y, the user is required to decide upon an appropriatespectral window for the analysis, and a priori values for com-ponent trace gas concentrations, pressure, temperature, path-length, and instrument line shape. From these, the forwardmodel generates a synthetic single-beam spectrum as a com-bination of a background spectrum (modelled as a polyno-mial) and the effect caused by gases having IR absorption



features within the spectral micro-window of interest. Calcu-lations are performed using the HITRAN database (Rothmanet al., 2009), listing absorption line positions and strengths,widths and details of pressure and temperature dependenciesfor the given species.

A polynomial function (the order of which is defined as aparameter by the user) is fitted to the measured spectrum andis used to simulate the 100% continuum line (i.e. the signalin the absence of the trace gas. Examples of different fit-ted polynomial functions are shown in Fig. 3. The forwardmodel calculates the optical depth (OD) of the target gas ateach wavenumberv as a function of the absorption coeffi-cient atv and the pathlength amount of each gas. A necessaryparameter for this computation is the Voigt line shape – theconvolution of the Doppler broadening Gaussian line shapefunction and the pressure broadening Lorentzian line shapefunction. The former is calculated using temperature andmolecular weight, and the latter using the pressure depen-dence given in HITRAN. Convolving the line strengths fromHITRAN with the line shape produces the absorption coeffi-cient used to calculate the optical depth. At wavenumberv,the overall OD is taken as the sum of all calculated ODs forall absorption lines for all species. The OD is then convertedto a transmission measure and convolved with the instrumentline shape (ILS) and the 100% continuum line to yield thefinal synthetic single-beam spectrum for the spectral windowof choice (Fig. 3). The ILS is dependent on the apodizationfunction used, the instrument field-of-view (FOV), and anymodulation loss or phase error in the interferometer. Theseparameters can be retrieved during the NLLS fitting proce-dure.

The difference between the synthetic and measured spec-trum yields a residual spectrum (Fig. 3, bottom); and thechi-squared (χ2) statistic and the partial derivatives for eachof the input parameters are calculated. The Levenburg-Marquardt method (Levenburg, 1944; Marquardt, 1963;Press et al., 1992) is used to find the least-squares linear bestfit, and thus the set of optimum gas concentrations that min-imise the residual spectrum, based on pre-determined con-vergence criterion (χ2 minimum).

4.2 Reported error

As with other spectrally-based retrieval approaches based onforward modelling and nonlinear fitting methods (e.g. Bur-ton, 1998), MALT reports the standard error for each of theretrieved trace gas amounts and the a priori input parame-ters (this metric is termed the reported error hereafter). Foreach iteration of the NLLS fitting procedure, the covariancematrix is determined from the standard deviation of the resid-ual spectrum (i.e. the synthetic spectrum subtracted from themeasured spectrum). The reported error for parameterxi isdefined as the square root of thei-th diagonal element ofthe covariance matrix, and is influenced by choice of a priorifixed input parameters, model errors/lack of fit, measurement

Fig. 3. Examples of results from a measured spectrum and the best-fit modelled spectrum produced using the MALT forward modeland nonlinear least squares (NLLS) fitting procedure described inGriffith (1996). The case shown is for 482 ppmm of CO at a gaspressure of 1000 hPa. Top: The measured and best-fit modelledspectra are shown to be well matched, with the different backgroundpolynomial functions (orders 1–5) tested also shown. The fourth or-der polynomial provided the best match to the measured spectrum,and this was used to simulate the best-fit modelled spectrum shown.Bottom: The residual spectrum (i.e. the measured spectrum sub-tracted from the modelled spectrum), which is used to provide ameasure of fitting accuracy. The spectral features in the residual aredue to an imperfect fit between the modelled ILS and the non-idealinstrument ILS.

noise, amount of information (the width of the spectral win-dow and intensity of signal within that window) and degreesof freedom (which reduces with increasing number of param-eters).

The reported error is based on the quality of the fit betweenthe measured and modelled spectra, and is in part designed toprovide the user with information potentially useful in gaug-ing the quality of the retrieval process. Most ideally the userwould like to know the actual retrieval error, i.e. the true dif-ference between the amount of trace gas present in the op-tical path and that reported by the retrieval procedure. Thisretrieval error can have both random and systematic com-ponents, and improved understanding of the relationship be-tween the reported error and retrieval error is one of the keyaims of this work, along with an appreciation of the absoluteaccuracies able to be obtained from the method, and theirsensitivity to model parameterisation uncertainty.



5 Methodology

5.1 Determination of input parameters

When performing a spectral fit, the input parameters requiredby the spectral model (MALT) can be stated as fixed con-stants or can be included in the fitting process. These pa-rameters relate to the composition of the sample atmosphere(i.e. which gases are present in the sample and have absorp-tion lines in the spectral window of interest, the concentrationof these gases, and the temperature and pressure of the com-position) and to the instrument line shape (i.e. spectral shift,resolution, apodisation, FOV, phase and zero-line offset). Inour experiment, whilst the gas concentration was fitted, thetemperature and pressure of the sample were taken from thegas cell PRT and Baratron readings respectively. Determina-tion of instrument line shape parameters was, however, lessstraight forward:

– the spectral shift (correction for fractional wavenumbershifts in the position of absorption lines caused by inac-curate knowledge of the interferometer alignment) wasfitted

– the spectral resolution was fixed at the manufacturer’sspecification (0.5 cm−1)

– asymmetry in the line shape influenced by smallchanges in spectrometer alignment was also fittedthrough a variable phase error

– the field-of-view (determined by the spectrometer’s lim-iting aperture and collimator focal length) was ini-tialised at the manufacturer’s specification and fitted asdescribed below to determine the effective value.

Horrocks et al. (2001) demonstrate that their MIDAC spec-trometer’s effective field-of-view of 52 mrad differed signifi-cantly from the nominally quoted 20 mrad. We followed themethodology of Horrocks et al. (2001) to determine the field-of-view of the instrument used here, measuring the spec-trum of CO gas with narrow absorption lines at low pressure(401 hPa) so that the resulting measurement is primarily afunction of the absorption feature convolved with the instru-ment line shape. 80 scans were co-added to create one par-ticularly low-noise spectrum. A series of MALT retrievalswere run for a single absorption line at 2082 cm−1, and thefield-of-view parameter optimised to give the lowest reportederror, whilst all other parameters remained fixed. The FOVparameter yielding the smallest reported error for the low-pressure CO absorption line was used as a fixed input forall other retrievals conducted here. Sensitivity to this param-eter was also investigated (see Sect. 5.3).To determine theretrieval error of the reported concentrations, it is necessaryto compare the retrieved concentrations with the true con-centration (i.e. to the cell concentrations listed in Table 1).

Retrieval error is therefore here defined as the true concen-tration subtracted from the reported concentration, dividedby the true concentration and expressed as a percentage.

One further consideration for the retrieval procedure is toaccount for any zero-baseline spectral offset that may resultfrom photometric errors associated with the use of an MCTdetector (Muller et al., 1999). Two factors might lead to anon-zero signal in spectral regions that should otherwise ex-hibit complete absorption. The first is caused by scatteringof radiation that has not originated from the lamp source, po-tentially related to imperfections in instrument optics, suchas dirty mirrors. This is a common occurrence in well usedfield spectrometers, particularly when deployed to dusty orcorrosive environments. Furthermore, if the gas cell was ata different temperature to that of the interferometer, an ef-fect will appear in the measured spectrum. Whilst laboratoryspectrometers often solve this problem by placing the inter-ferometer before the sample cell, this is not of the case forbistatic OP-FTIR field configurations (Muller et al., 1999).Neither the temperature of the gas cell nor spectrometer werecontrolled in this experiment, but were rather left to equili-brate to ambient temperature, and therefore small differencesin temperature may have influenced the recorded spectra.The second factor which might lead to a non-zero baselineis detector saturation. MCT detectors saturate rather easily(Smith, 1995), and whilst efforts were made in this study toprevent detector saturation via use of the attenuator, somedetector saturation effect may be present. Any zero-baselineoffset caused by stray light or detector saturation will be ap-parent in spectral regions where the examined gases shouldabsorb all incoming radiation (e.g. the CO2 saturation bandat ∼2350 cm−1). If an offset was present, this amount wassubtracted from the spectrum before quantitative analysis.

5.2 Spectral window and “background” polynomial

MALT requires the user to select a suitable spectral windowand an appropriate polynomial for simulating the continuumspectra. To yield the most accurate concentrations, the win-dow must have sufficient information about the gas of in-terest (i.e. an absorption feature) and should ideally be ina region of the IR spectrum that minimises contaminatingabsorption features from other gases (though this is not es-sential). The order of the polynomial used to simulate thecontinuum spectrum needs to be carefully selected so that itdoes not fit broad absorption features. In this work, a seriesof spectral windows were tested for retrieving the concentra-tions of each gas (Fig. 4 and Table 2), and the window yield-ing the lowest retrieval errors was thus identified. Similarly, arange of polynomial orders (3rd, 4th and 5th order) were em-ployed. Given that all three gases in this study demonstratefine absorption structure (a number of clearly defined narrowabsorption lines) within the tested spectral windows, it is un-likely that the background polynomial fit will be influenced



Fig. 4. Modelled and measured spectra at 0.5 cm−1 wavenumber resolution for the CO2, CH4, and CO trace gases considered here. (left)Absorbance spectra modelled using the MALT forward model; (right) Measured FTIR single-beam spectra. The various spectral windowsused to retrieve the trace gas concentrations from the measured spectra are indicated by the numbered horizontal arrows in(d), (e), (f) andare detailed in Table 2.

by these, except perhaps across the narrow CH4 spectral win-dow.

For CO2 (Fig. 4a and d), the widest spectral spectral win-dow used here, 2020–2310 cm−1 (taken from Esler et al.,2000) was split into two sub windows, 2150–2310 cm−1

(location of primary absorption features of13CO2 and12CO2) and 2034–2075 cm−1 (location of the weaker12CO2feature, see inset in Fig. 4a). For each window, CO2 retrievalswere run using a background continuum spectrum simulatedvia 3rd, 4th and 5th order polynomials. Given that water



Table 2. Spectral windows used here for the retrieval of CO2, CH4and CO and marked in Fig. 4. Also listed are the potentially interfer-ing gases (those in brackets were not included in the forward-modelspectral simulation conducted here due to the very short clean airatmosphere path used, but would generally be required over longerpathlengths in the ambient atmosphere).

Target Gas Spectral window Interfering gases

CO2 2020–2310 cm−1 H2O (N2O, CO)2034–2075 cm−1 H2O2150–2310 cm−1 H2O (N2O, CO)

CH4 2894–3001 cm−1 H2O2980–3090 cm−1 H2O3005–3020 cm−1 H2O

CO 2000–2230 cm−1 H2O2039–2057 cm−1 H2O2142–2241 cm−1 H2O

vapour was certainly present in the ambient part of the pathexternal to the gas cell and has absorption lines in these spec-tral windows, H2O was also included in the retrievals. WhilstCO and N2O also absorb within these spectral windows, theywere not present in sufficient amounts to be significant. Infield situations using longer pathlengths, CO and N2O mayaffect the measured signal and should therefore be includedin any retrieval procedure. For CH4, Esler et al. (2000) use abroad spectral window, 2810–3150 cm−1. Unfortunately, themajority of this window is affected by a spectrometer arte-fact (2800–2990 cm−1, see Fig. 4b and e), believed to becaused by residue on the instrument optics. The complex-ity introduced by the artefact significantly hinders the abil-ity to model the spectrum using a lower-order (<6) polyno-mial. Two spectral windows were therefore selected so as toexclude the effects of this artefact, a broad window (2980–3090 cm−1), that maximises the number of CH4 absorptionlines, and a narrower window concentrating on the strongestlines (3005–3020 cm−1). In addition, a third window, lyingwithin the region where lines are affected by the detectorartefact (2894–3001 cm−1) was also investigated. For CO(Fig. 4c and f), Esler et al. (2000) use a broad window en-compassing the entire CO absorption feature and a similarwindow is used here (2000–2230 cm−1). In addition, twonarrower windows, one featuring only one branch of the COabsorption feature (2142–2241 cm−1) and the other featur-ing only four weaker CO absorption lines (2039–2075 cm−1)were also investigated.

5.3 Sensitivity analysis and error budget

A local sensitivity analysis was performed in order to de-termine the influence of model parameter uncertainty on

retrieval accuracy. Uncertainties in temperature, pressureand spectrometer FOV were considered, which may resultfrom field situations where the measurement conditions areless tightly controlled than is possible in the laboratory. Inparticular, it can be difficult to measure temperature andpressure precisely in some open-path geometries, particu-larly when analysing high altitude plumes, or ones wherethe plume is generated by high temperature volcanological orcombustion-related processes. Pressure and temperature areimportant in the retrieval procedure as they affect the shapeof gas absorption features upon which the fit between themeasured and modelled spectra depends. Assumed pressuredetermines the Lorentzian line shape of absorption lines inthe simulated spectra. Higher pressures lead to a broadeningof line widths, and the maximum line depth is suppressed.Whilst the relatively low (0.5 cm−1) spectral resolution of theFTIR spectrometer used here is responsible for the majorityof observed linewidths, this pressure-related broadening doesalso influence the retrieval process. Pressure broadening forany sample gas is also related to the other gases contained inthe gas mixture.

The influence of assumed temperature is to affect thestrengths of individual absorption lines and the band shapeof the modelled spectra. Doppler broadening caused by thetemperature-dependent distribution of molecular velocitieswithin gases (as well as a minor influence on line broad-ening) contributes to the temperature dependence of line-shapes. The primary influence of temperature and pres-sure, however, is in the calculation of the mixing ratiofrom the retrieved number of gas molecules per square cm(molecules cm−2) output from the retrieval process (the ab-sorption features present in the spectra are a direct functionof the number of molecules of the target gas in the opti-cal path). The relationship between the concentration of aparticular gas in a sample, in molecules per square centime-tre (X, molecules cm−2) and the mixing ratio of the gas (x,ppm), pressure (p, hPa), temperature (T , K) and pathlengthof the sample (L, m) is described in Eq. (5), whereA is Avo-gadro’s constant (6.022× 1023 mol−1) andR is the gas con-stant (8.314 J [mol K]−1):

X =xLpA

RT(5)

Any error in assumed pressure or temperature will there-fore cause a proportional error in retrieved mixing ratio (x)through Eq. (5); whereas, retrievals in molecules cm−2 willonly be affected by the influence of pressure and temperatureerrors on the modelled spectra. In many applications, OP-FTIR is used to investigate concentration ratios of two gases,for example CO2:CO in biomass burning studies (Yokelsonet al., 1997) or SO2:HCl in volcanological applications (Bur-ton et al., 2007), and in this case it may not be necessary toretrieve volumetric mixing ratios since the ratios of the gasamounts expressed in units of molecules cm−2 or ppmm isidentical. Therefore, for the sensitivity analysis conducted



Fig. 5. Sensitivity of the reported error (based on the fit residuals)and retrieval error (based on the difference between retrieved path-length trace gas amount and actual pathlength trace gas amount) toassumed instrument FOV. The example is shown for CO trace gasretrievals based on the CO absorption line centred at 2082 cm−1

(Fig. 6). Measurements were made at a low pressure of 400.5 hPawith a true CO mixing ratio of 1217.05 ppm. Reported error is min-imised at an assumed FOV of 22 mrad, though is relatively insen-sitve to the FOV variations studied here. Retrieval error is, howeversignificantly more sensitive, and assumed 20 mrad FOV yields thesmallest actual retrieval error.

here, pressure and temperature-independent amounts (inmolecules cm−2) were used for the comparison. Pressureand temperature inputs were varied systematically by up to±20◦C and ±200 hPa respectively; ranges that might befound over altitude differences of up to 3 km. Retrieved con-centrations were compared with true concentrations to yieldboth the retrieval error and sensitivity to the pressure andtemperature assumptions.

6 Results and discussion

6.1 FOV determination

Figure 5 shows how the reported error (i.e. the MALT fittingerror, quantified as a percentage of the retrieved concentra-tion in Sect. 4.2) and the actual retrieval error (quantified asthe percentage difference between the retrieved gas concen-tration and the true gas concentration in Sect. 4.2) varies withassumed field-of-view. Actual retrieval error is much moresensitive to FOV variations than is the reported error. Thelowest reported error occurs at a FOV of 22 mrad, whereasthe lowest retrieval error occurs at a FOV of 20 mrad. As-sumed FOV significantly larger or smaller than the 22 mradoptimum value resulted in increasingly poor fits between themodelled and measured CO spectrum (Fig. 6). Unlike Hor-rocks et al. (2001), we found the optimal FOV, according to

Fig. 6. Measured single-beam spectra and best-fit modelled spectrafor the CO absorption line centred at 2082 cm−1 at a gas pressureof 400.5 hPa. Modelled spectra were simulated assuming differentfields-of-view (15–25 mrad), with the 22 mrad FOV providing thebest match between the measured and modelled spectra.

the reported error, to be similar to the nominal FOV statedby the instrument manufacturer, and we attribute the 2 mrad(10%) discrepancy to off-axis rays caused by a combinationof small misalignments of spectrometer and telescope optics,and an imperfect source collimator. Horrocks et al. (2001)also found a discrepancy between the FOV parameter yield-ing the lowest reported error and those that yielded the low-est retrieval error. This discrepancy may be explained byour use of nitrogen as a buffer gas, given that line broad-ening coefficients in the HITRAN08 database (Rothman etal., 2009) relate to the gas of interest in air, and not whenmixed with nitrogen. The difference between nitrogen andair broadening is of the order of∼10%. This factor, com-bined with uncertainties in HITRAN, or an inability of theforward modelling and NLLS fitting procedure to accuratelyretrieve concentrations using a single absorption line giventhe relatively low spectral resolution of the instrument, mayalso explain this discrepancy. By retrieving concentrationsusing broader spectral features, the retrieved effect of instru-ment line shape inaccuracies on individual absorption linesare decreased. The effects of degrading the assumed spec-tral resolution from the highest 0.5 cm−1 value were investi-gated, but increased the reported errors, and therefore furtheradjustments to this factor were not required.

6.2 Spectral window and background polynomial

6.2.1 Carbon dioxide

For each gas, three spectral windows were identified con-taining either a broad absorption feature or a selection of



Fig. 7. Retrieval errors for CO2, CH4 and CO trace gas retrievals resulting from use of the MALT model and NLLS fitting procedure withOP-FTIR spectra from a gas cell containing samples of these three gases over wide concentration ranges. Retrievals were made using threedifferent spectral windows for each trace gas and three different polynomial orders. In order to aid comparison of the error magnitudes forthe retrievals of each trace gas, the same y-axis range is used to display the results from the three spectral windows tested. Retrieval errormagnitude is seen to vary quite widely between the different spectral windows used to retrieve the pathlength amount of a particular tracegas, and for some windows between the different polynomial orders examined.

individual absorption lines (Fig. 4 and Table 2). For CO2,results shown in Fig. 7 indicate that the absolute retrieval er-ror for 5 of the 6 pathlength amounts tested is at a minimumfor the 2150-2310 cm−1 spectral window using a fourth-order polynomial, with retrieved pathlength amounts over thefull range tested having a root mean squared (RMS) error of2.4% (Fig. 7b). Whilst the results show little sensitivity tothe use of a fourth or fifth-order polynomial, the use of athird-order polynomial leads to a noticeable increase in re-trieval error. A third-order polynomial is insufficient to de-scribe the background shape of a spectral window as wide as2150–2310 cm−1. Moreover, the background shape of thiswindow is complicated by the CO2 absorption feature thatstrengthens to saturation at 2310 cm−1 (Fig. 4a). Retrievalerrors are highest for the broader, 2020–2310 cm−1 spec-tral window (Fig. 7a), though the reported error (not shown)

is lowest for this window (0.1%, compared with 0.3% for2150–2310 cm−1 and 0.9% for 2034–2075 cm−1). This ap-parent contradiction may be explained by the presence of alarge featureless baseline across most of this wider spectralwindow (Fig. 4a) leading to an overall improved fit betweenthe modelled and measured spectrum, though not necessar-ily the best fit at the wavenumber location of the absorptionfeatures. A wider spectral window typically decreases theability of any particular polynomial to model the backgroundcontinuum as is the case here. There is also an additional rea-son why use of the broader spectral window generally leadsto greater inaccuracy. This is because the zero-baseline off-set can only be calculated from data collected in the CO2 ab-sorption saturation region (near 2350 cm−1), and uncertain-ties in this correction will increase as the offset is applied tomore distant spectral locations. The results for the narrowest



Fig. 8. Examples of measured spectra and best-fit modelled spectra made using the optimum spectral windows and a fourth-order polynomialbackground (top), and the residual between the measured and modelled spectra (bottom) for(a) CO2; (b) CH4; and(c) CO. Modelled spectrawere simulated using MALT and the best-fit modelled spectra were found using the NLLS fitting procedure.

spectral window (2034–2075 cm−1) used here for CO2 re-trieval are less influenced by the choice of polynomial order,each having RMS errors of less than 3.7% (Fig. 7c). Theflatter background continuum in this window, combined withthe presence of fine absorption structure in the CO2 lines, ex-plains the reduced sensitivity to polynomial order. The inac-curacy of the retrievals made at lower pathlength amounts inthis spectral window is most likely due to the weaker natureof the absorption lines at 2034–2075 cm−1.

Our results clearly indicate that the choice of spectral win-dow, coupled with an appropriate choice of background poly-nomial, have a strong influence on CO2 retrieval accuracy.Broader windows typically contain more information, poten-tially improving the fit between the modelled and measuredspectra. However, it is also important to ensure that the back-ground continuum of the spectrum within the window understudy can be sufficiently well represented by the chosen poly-nomial. Our results suggest that whilst the 2020–2310 cm−1

spectral window used for CO2 retrieval gives the lowest re-ported errors (based on the fit residuals; Sect. 4.2), it doesnot result in the lowest retrieval error. The 2150–2310 cm−1

spectral window, used with a fourth-order polynomial actu-ally provides the lowest retrieval error for CO2, ranging from−1.9% to 4.3% across all pathlength amounts tested. An ex-ample spectrum with best-fit modelled spectrum is shown inFig. 8a.

6.2.2 Methane

As outlined in Sect. 5.2, retrievals of CH4 were confoundedby an instrument artefact in the relevant absorption region.The spectral window tested that covered this region (2894–3001 cm−1) showed both large reported and retrieval errors,

regardless of the polynomial order chosen (Fig. 7e). Thelowest retrieval errors for CH4 come instead from the 2980–3090 cm−1 spectral window that excludes the artefact region(Fig. 7d), with a fourth-order polynomial yielding an RMSerror of 1.4% (Fig. 8b shows an example spectrum with abest-fit modelled spectrum for this spectral window). Aswas the case with the narrowest (2034–2075 cm−1) CO2 re-trieval window, the polynomial order does not significantlyinfluence retrieval accuracy due to the fine structure of theCH4 absorption lines and the flat background continuum.However, for the narrowest CH4 retrieval window tested(3005–3020 cm−1), the polynomial order has a strong in-fluence (Fig. 7f) with only a first order function allowingpathlength amounts to be retrieved within an RMS error of3.9%. Individual CH4 absorption lines remain unresolved atthe 0.5 cm−1 spectral resolution used here, and instead com-bine to appear as one large apparent absorption feature, andthus higher order polynomials incorrectly start to fit this fea-ture as well as the background continuum.

6.2.3 Carbon monoxide

Results for CO suggest that the two broadest spectral win-dows provide very similar retrieval accuracies (Fig. 7gand h), with the 2000–2230 cm−1 spectral window used witha fourth-order polynomial achieving an RMS error of 3.6%across all pathlength amounts tested here (slightly betterthan the RMS error of 3.9% for the 2142–2241 cm−1 spec-tral window). Figure 8c shows an example spectrum andbest-fit modelled spectrum for the spectral window 2000–2230 cm−1. Generally, the two narrower spectral windowsoverestimated pathlength amounts compared to the 2000–2230 cm−1 window. Retrievals for CO across all spectral



windows tested here showed a lower reliance on choice ofbackground polynomial compared to the other gases, reflect-ing the “flat” background continuum across the whole COabsorption feature (Fig. 4f). Results from the narrower 2039–2057 cm−1 spectral window indicate that it is best suited toretrieval of higher pathlength amounts (Fig. 7i), with poor re-trieval accuracies for pathlength amounts below 1000 ppmm.High reported errors (based on the fit residuals) suggest thatthe retrieval process performs poorly with the weak absorp-tion lines in this spectral window, as is also the case for lowerpathlength amounts of CO2 retrieved in the 2034–2075 cm−1

spectral window.

6.3 Sensitivity analysis and error budget

Using the optimum set of retrieval parameters described inSect. 6.2, a series of sensitivity analyses were performed. InSect. 6.1, the spectrometer FOV was determined as 22 mrad.The exact FOV is difficult to determine given the fast opticsand the absence of a well defined limiting aperture. We com-pared retrievals made using our optimally determined FOVwith those made using a FOV varied by±10%.

Retrievals for all three gases generally show a system-atic reliance upon the specified FOV (Fig. 9), with re-trieved pathlength amounts generally increasing with as-sumed FOV. CO demonstrated the greatest sensitivity to FOVsince the CO absorption lines are narrower than the instru-ment’s 0.5 cm−1 spectral resolution and their representationis therefore strongly influenced by instrument parameters.CO2 retrieval accuracy appears to be less sensitive to FOVuncertainty at higher pathlength amounts. This may be ex-plained by the increasing saturation (absorption of all sourceenergy) by strong absorption lines at higher CO2 pathlengthamounts, leaving fewer lines in the spectral window affectedby errors in FOV.

The retrieval sensitivities to assumed pressure and temper-ature were calculated from the pressure- and temperature-independent molecular amounts (molecules cm−2), ratherthan from the volumetric mixing ratios (ppmm), as the lat-ter are additionally sensitive to these parameters via the re-lationship used to interconvert between these two concentra-tion units (Eq. 5). Figure 10 shows the sensitivity of the re-trievals to assumed gas pressure, where it can be seen thatpathlength amounts are generally overestimated when pres-sure is underestimated, and vice versa. As is the case withthe FOV parameter, the modelled absorption line widths areaffected by the assumed pressure (Fig. 11a and b). Whena lower pressure is assumed, narrower lines than are actu-ally present in the measured spectrum are modelled due toinadequate pressure broadening, causing a positive residualbetween the modelled spectrum and the measurement (sim-ilar to the residual spectrum in Fig. 11b. In order to fit themodelled spectrum to the measured spectrum, the NLLS pro-cedure increases the concentration of the absorber to min-imise this positive residual, leading to an overestimation of

Fig. 9. Sensitivity of trace gas concentration retrieval error to theassumed FOV for(a) CO2, (b) CH4, and(c) CO. Retrievals weremade using the MALT model with a NLLS fitting procedure. Thesame y-axis range is used in each case to aid comparison of errormagnitude between gases.



Fig. 10. Sensitivity of trace gas concentration retrieval error to theassumed gas pressure for(a) CO2, (b) CH4, and(c) CO. Retrievalswere made using the MALT model with a NLLS fitting procedure.The same y-axis range is used in each case to aid comparison oferror magnitude between gases.

gas pathlength amounts, whereas the reverse is true when as-sumed pressure is overestimated.

For CH4 and lower pathlength amounts of CO, the error in-duced by pressure uncertainties was significantly lower thanfor CO2 (Fig. 10). As pathlength amounts increase, absorp-tion lines deepen, causing any line shape inaccuracies dueto incorrect pressure specification to be exacerbated. ForCO2, line deepening is less of an issue, given that deep ab-sorption lines occur for all pathlength amounts in the spec-tral window chosen, and this explains why CO2 retrievalsshows a higher sensitivity to pressure uncertainties at allpathlength amounts, with the percentage error relatively in-dependent of actual concentration. We find that the reportederrors based on the modelled fit residuals show little depen-dence on pressure (±0.04%,±0.01% and±0.002% across±100 hPa for CO2, CH4 and CO respectively), whereas re-trieval errors show a much greater sensitivity. In field sit-uations, pressure uncertainties are most likely to arise fromuncertainty in plume height. Our analysis shows that uncer-tainties of up to 500 m at sea level (∼50 hPa) are thereforeequivalent to a±0.5% uncertainty in CH4 and low CO path-length amounts, but are closer to±3% for CO2 and higherpathlength amounts of CO.

Figure 12 shows the sensitivity of retrieved pathlengthamount to assumed temperature. For CH4 and CO re-trievals, temperature increases lead to proportional in-creases in retrieved pathlength amounts, whilst for CO2,this effect is not observed at lower pathlength amountsand is reversed for the highest pathlength amounts (above5× 1020 molecules cm−2). These findings are best explainedby the temperature dependence of spectral band shape.Changing temperature affects the envelope of the absorptionband (Fig. 11c), with higher temperatures causing more ab-sorption in the weaker lines that lie towards the edge of theband, and reduced absorption in the stronger lines locatedtowards the middle of the band. Therefore, for spectral win-dows containing strong absorption lines located towards themiddle of an absorption band, when assumed temperatureis overestimated, a higher gas concentration is required forthe modelled spectrum to best-fit the measured spectrum.When a spectral window containing weaker absorption linesat the edge of an absorption band is used, the opposite istrue. For the CH4 and CO spectral windows, these effectslargely cancel each other out as the spectral windows lieacross both strong and weaker lines at the middle and edgeof their respective absorption bands. The greater influenceof the stronger absorption lines leads to a small positive sen-sitivity for CH4 and CO in the spectral windows used here.For CO2, however, the saturation of the strongest lines to-wards the middle of the band means that the sensitivity ofconcentration retrievals to temperature is reversed.



Fig. 11. Simulated transmission spectra for CO gas at a fixed molecular amount of 6.424× 1017molecules cm−2, along with percentagedifference in transmission between the CO transmission spectra simulated using(a) an assumed FOV of 15 mrad and 25 mrad;(b) at 600 and1200 hPa; and(c) at 270 K and 330 K. The figure focuses on thep-branch of the CO vibrational stretching mode absorption feature, centredat 2143 cm−1. Increasing FOV leads to broader, but weaker absorption lines; increasing pressure leads to deeper and broader absorptionlines; whilst increases in temperature lead to stronger absorption towards the edge of the band (wavenumbers< 2100 cm−1) and weakerabsorption towards the band centre (wavenumbers> 2100 cm−1).

6.4 Sensitivity summary

Table 3 summarises the findings of the sensitivity analysesand indicates to what percentage accuracy CO2, CH4 and COcan be retrieved assuming optimum parameterisation of theforward model. The “worst-case” scenario (as suggested byHorrocks et al., 2001) indicates that the total error due to un-certainties that could arise from incorrect retrieval parame-terisation amounts to less than 8.2% for all tested pathlengthamounts, with a mean of 4.8%. Generally these “external”errors are of a similar magnitude to the additional errors thatmaybe introduced via the uncertainty inherent in the absorp-tion line intensities for each gas. The HITRAN08 absorptionline intensity uncertainties are reported to be between 5–10%for CO2 and CH4, but are lower for CO at 1–2% (Rothmanet al., 2009). Of course, with good meteorological measure-ments and careful collection of non-saturated single-beamspectra, the magnitude of the external errors can be min-imised. Whilst a global/variance-based sensitivity analysismay theoretically offer the potential to provide further in-formation about the effects of simultaneous uncertainties inmultiple inputs (e.g. Petropoulos et al., 2009), the linear sen-sitivity of the output gas amounts to uncertainties in the threeinput parameters suggests that the local sensitivity analysisperformed here is perfectly adequate for our purposes.

Errors in assumed pressure become increasingly signifi-cant at higher pathlength amounts, due to the deepening ofabsorption lines, especially for CO2 and CO. One solutionto this problem would be to use a spectral window withweaker absorption lines; however, the results for tempera-ture sensitivities indicate that this would increase sensitivityto the spectral band shape dependence on temperature. Er-rors in assumed temperature of less than 10◦C lead to er-rors in retrieved concentration of below 3%. Greater errorsare perhaps most likely to occur during studies focused on

plumes from hot sources (volcanic, fire or industrial), andcare should be taken to minimise sensitivity to these errorsby using a broad spectral window encompassing weak andstrong absorption lines and ideally targeting plumes oncethey have cooled to near ambient temperatures at some dis-tance from the source region.

In our experiment, the spectrometer FOV was determinedto be 10% higher than the manufacturer’s nominal value of20 mrad. Unlike gases such as SO2, ambient and elevatedpathlength amounts of CO2, CH4 and CO demonstrate deepabsorption lines that increase their sensitivity to instrumentline shape, and therefore extra care should be taken to pre-serve instrument optics from degradation if measurementsare to target these gases.

7 Summary and implications for field measurements

We investigated the accuracy of trace gas retrievals made us-ing a field-portable FTIR spectrometer under conditions thatreplicated those likely to be encountered in many field sit-uations, e.g. uncertain gas temperature, pressure and instru-ment line shape/FOV characteristics, and attempted to de-termine the optimum spectral window within which the re-trieval should be made under different measurement condi-tions. Our study was based on the measurement of gasescontained within a 1 m gas cell, from which we collected0.5 cm−1 wavenumber resolution single-beam IR spectra ofCO2, CH4 and CO over a very broad range of pathlengthamounts, representing equivalent mixing ratios from thosefound in the clean, ambient atmosphere to the highly pol-luted plumes of biomass burning, volcanoes and industryover pathlengths of tens to hundreds of metres (Table 1).

We used a modelling nonlinear least squares fitting ap-proach to retrieve the concentration of each target gasspecies. A number of spectral windows were investigated,



Fig. 12. Sensitivity of trace gas concentration retrieval error to theassumed gas temperature for(a) CO2, (b) CH4, and(c) CO. Re-trievals were made using the MALT model with a NLLS fitting pro-cedure. The same y-axis range is used in each case to aid compari-son of error magnitude between gases.

Fig. 13. Relationship between mean retrieved pathlength trace gasamounts made using the optimum parameterisation of the MALTmodel determined herein. The 1:1 line is shown and all retrievedamounts are within 4.8% of true amounts (note logarithmic axes).

and those that maximised the amount of absorption informa-tion for each gas (e.g. the number of absorption lines) typi-cally produced the lowest reported errors (model fit residu-als) and the lowest actual retrieval errors when compared tothe true gas cell pathlength amount. However, if broad spec-tral windows are to be used it is important to ensure a goodbackground polynomial fit in the model (which is used torepresent the continuum radiation), and we found that whenwider windows were investigated, containing large regionsshowing no absorption (e.g. 2020–2310 cm−1 for CO2), re-trieval accuracies were degraded due to poor background fit-ting. Similarly, it is important to check that broader win-dows do not contain spectral artefacts, such as those foundhere in the 2894–3001 cm−1 spectral window when retriev-ing CH4. Such artefacts, potentially caused by contaminatingsubstances on the spectrometer optics, will complicate thesimulation of the continuum background shape using lower-order polynomials, and should be carefully avoided.

When using the optimum parameterisation of the MALTforward model and nonlinear least squares fitting proceduredeployed in the retrievals made here, we were able to retrievetrace gas pathlength amounts to within 4.8% of the true val-ues for all gases and pathlength amounts tested (Fig. 13).Mean retrieval errors were 2.4%, 1.4% and 3.6% for CO2,CH4 and CO, respectively. A series of analyses was per-formed to assess the sensitivity of these retrievals to uncer-tainties in instrument (i.e. FOV) and environmental (i.e. tem-perature, pressure) parameters. The uncertainties assumedwere of a magnitude similar to those expected in the types offield situations in which OP-FTIR may be employed. Sensi-tivities were shown to vary between target gases. Uncertaintyin the FOV had most impact on CO retrieval. This is becausethe shape of the modelled CO absorption feature is highly



Table 3. Summary of errors associated with parameter uncertainty when retrieving trace gas amounts from OP-FTIR measurements usingthe MALT foward model of Griffith (1996) with a NLLS fitting procedure. Errors for choice of polynomial and errors in assumed field-of-view, pressure and temperature are taken from the results presented in Figs. 7, 9, 10 and 11, and are calculated using the difference betweenthe retrievals made using the best parameter to those using the altered parameter, expressed as a percentage. For example, at an actualCO2 pathlength amount of 12 612 ppmm, the retrieved CO2 column amount based on the retrieval method parameterised with the optimumparameter values was underestimated by just under 2%. Uncertainties in the HITRAN08 database (Rothman et al., 2009) refer to the lineintensity error specified therein.

Retrieval Error (%), for CO2 pathlength amounts (ppmm):Source of Error 12 612 26 235 48 080 105 112 210 172 357 304

Choice of polynomial (4th or 5th order) 0.9 0.6 1.7 1.8 1.5 0.9Field-of-view (best-fit or manufacturer’s) 5.2 6.2 5.5 3.2 0.2 1.850 hPa error in assumed pressure 2.2 2.8 3.2 2.1 3.4 3.510◦C error in assumed temperature 4.2 4.5 1.0 2.5 0.6 4.3Total (added in quadrature) 7.1 8.2 6.7 4.9 3.8 5.9Uncertainty in line intensities (HITRAN08) 5.0–10.0 5.0–10.0 5.0–10.0 5.0–10.0 5.0–10.0 5.0–10.0Mean reported error 0.2 0.3 0.4 0.4 0.3 0.3Optimum retrieval model parameters −1.9 3.1 4.3 −1.0 −1.7 2.7

Retrieval Error (%), for CH4 pathlength amounts (ppmm):54.5 97.4 176.9 284.3 514.5

Choice of polynomial (4th or 5th order) 1.6 0.8 0.6 0.7 1.0Field-of-view (best-fit or manufacturer’s) 2.4 1.6 1.4 1.3 1.250 hPa error in assumed pressure 0.8 0.4 0.3 0.3 0.610◦C error in assumed temperature 2.8 2.2 2.1 1.9 1.5Total (added in quadrature) 4.1 2.9 2.6 2.4 2.2Uncertainty in line intensities (HITRAN08) 5.0–10.0 5.0–10.0 5.0–10.0 5.0–10.0 5.0–10.0Mean reported error 2.0 0.9 0.6 0.6 0.8Optimum retrieval model parameters 0.8 0.2 0.1 4.8 1.3

Retrieval Error (%), for CO pathlength amounts (ppmm):19.9 256.3 482.0 1,277.7 6,379.9

Choice of polynomial (4th or 5th order) 0.2 0.0 0.0 0.0 0.0Field-of-view (best-fit or manufacturer’s) 4.0 5.4 5.4 5.1 2.450 hPa error in assumed pressure 1.7 0.5 1.3 2.8 4.310◦C error in assumed temperature 0.2 0.8 0.9 1.0 1.0Total (added in quadrature) 4.4 5.5 5.6 5.9 5.0Uncertainty in line intensities (HITRAN08) 1.0–2.0 1.0–2.0 1.0–2.0 1.0–2.0 1.0–2.0Mean reported error 0.5 0.1 0.1 0.1 0.1Optimum retrieval model parameters −4.0 4.4 4.3 2.0 3.4

dependent on the assumed instrument FOV, due to the partic-ular narrowness of the CO absorption lines which remain un-resolved at the 0.5 cm−1 resolution used here. The sensitivityof all retrievals to FOV increased when the spectral windowused for the analysis contained strong absorption lines, whichoccurred at higher pathlength amounts for the CH4 and COspectral windows, but at lower pathlength amounts for theCO2 spectral window (where higher pathlength amounts ledto absorption saturation, and therefore, a smaller number ofobserved absorption lines).

Generally, our results indicate that reported errors, whichare based on the residuals between the best-fit forward mod-elled spectra and the measured spectra, are smaller than theactual retrieval errors and do not always vary in the same

manner (Table 3). Reported errors should therefore not beregarded as a proxy for actual retrieval error. Reported er-rors appear most useful for the optimisation of instrumentline shape, where minimising the reported error via adjust-ment of the assumed FOV can improve actual retrieval errors.However, errors in assumed FOV, temperature and pressurecan all impart similar effects on the spectral fitting. For ex-ample, minimising reported errors by adjusting the assumedpressure could improve the spectral fit, but the same degreeof improvement might be achieved by adjusting the FOV, po-tentially resulting in a quantitatively different retrieved path-length trace gas amount. These sensitivities and uncertain-ties suggest that proper assessment of gas temperature, pres-sure and instrument FOV are important for accurate trace gas



concentration retrieval, given that errors induced by one pa-rameter may be compensated for by adjusting the value ofanother parameter to minimise reported error, but that thismay result in an incorrect retrieval.

We found that retrieval sensitivity to uncertainties in tem-perature and pressure were relatively small for the magni-tude of parameter uncertainty that might be expected in typ-ical field situations. Assuming a potentially “worst-case”scenario of a 50 hPa and 10◦C error in assumed pressureand temperature, and the 10% difference in FOV found hereas compared to the instrument manufacturer’s specification,pathlength amount retrievals might vary by up to 8.2% (er-rors added in quadrature). As discussed by Horrocks etal. (2001), gases that demonstrate individual absorption linesthat are resolved in the spectra (as opposed to gases such asSO2, which has broad bands for which individual rotationallines cannot be resolved), are more susceptible to parametererrors affecting spectral line shape. Minimising uncertaintyin these parameters is therefore paramount for retrievals ofCO2, CH4 and CO via a combination of accurate temper-ature and pressure information, and careful examination ofthe spectral fit. In particular, as demonstrated in this study,errors due to poor zero-baseline offset correction, incorrectpressure, temperature, and instrument line shape assump-tions will all cause a poor fit when a retrieval is performedusing a window containing both weak and strong absorptionlines, and minimising reported errors in such a window willimprove retrieval accuracy.

Our results confirm that a forward modelling approachcoupled with a nonlinear least squares fitting routine can be aviable and accurate method for retrieving gas concentrationsfrom OP-FTIR data, in this case using an MCT detector cov-ering a wide spectral range (600–6000 cm−1). Whilst it re-mains difficult to use the reported errors (model fit residuals)to provide a quantitative measure of actual concentration re-trieval error, our results provide confidence that carefully un-dertaken retrievals made using the forward modelling NLLSmethod deployed here can indeed provide good retrieval ac-curacies in the types of field situation where OP-FTIR couldbe very usefully deployed. Using an optimum parameterisa-tion of the model, we were able to retrieve the concentrationsof the three most abundant carbonaceous gases in the atmo-sphere to better than 5% over a very wide range of pathlengthamounts (Fig. 13).

Acknowledgements.We would like to thank NERC MSF and theirstaff at RAL, particularly Robert McPheat and Kevin Smith, fortheir invaluable contribution to the experimental component ofthis work, and Christopher MacLellan and Alasdair MacArthur ofNERC FSF for their wide ranging support, including loan of theFTIR spectrometer used here. We are very grateful for the expertiseprovided by Peter Zemek and Don Mullally (MIDAC Corporation),Clive Oppenheimer (University of Cambridge) and Mike Burton(Istituto Nazionale di Geofisica e Vulcanologia) at various pointsduring the study, including during parts of the measurementcampaign. Funding for the studentship of T. E. L. Smith comes

from NERC/ESRC Studentship ES/F012551/1. The contributionof Martin Wooster was supported by the NERC National Center forEarth Observation (NCEO).

Edited by: D. Feist

References

Bacsik, Z., Mink, J., and Keresztury, G.: FTIR spectroscopy of theatmosphere I. Principles and methods, Appl. Spectrosc. Rev., 39,295–363, 2004.

Bertschi, I., Yokelson, R. J., Ward, D. E., Babbitt, R. E., Su-sott, R. A., Goode, J. G., and Min Hao, W.: Trace gasand particle emissions from fires in large diameter and be-lowground biomass fuels, J. Geophys. Res., 108(D13), 8472,doi:10.1029/2002JD002100, 2003.

Briz, S., de Castro, A. J., Dıez, S., Lopez, F., and Schafer, K.:Remote sensing by open-path FTIR spectroscopy, Comparisonof different analysis techniques applied to ozone and carbonmonoxide detection, J. Quant. Spectrosc. Ra., 103, 314–330,2007.

Burton, M. R.: Remote sensing of the atmosphere using Fouriertransform spectroscopy, PhD thesis, Department of Chemistry,University of Cambridge, 1998.

Burton, M. R., Allard, P., Mure, F., and La Spina, A.: Magmatic gascomposition reveals the source depth of slug-driven strombolianexplosive activity, Science, 317, 227–230, 2007.

Childers, J. W., Thompson Jr., E. L., Harris, D. B., Kirchgess-ner, D. A., Clayton, M., Natschke, D. F., and Phillips, W. J.:Multi-pollutant concentration measurements around a concen-trated swine production facility using open-path FTIR spectrom-etry, Atmos. Environ., 35, 1923–1936, 2001.

Childers, J. W., Phillips, W. J., Thompson Jr., E. L., Harris, D. B.,Kirchgessner, D. A., Natschke, D. F., and Clayton, M.: Compar-ison of an Innovative Nonlinear Algorithm to Classical Least-Squares for Analyzing Open-Path Fourier Transform InfraredSpectra Collected at a Concentrated Swine Production Facility,Appl. Spectrosc., 56(3), 325–336, 2002.

Esler, M. B., Griffith, D. W. T., Wilston, S. R., and Steele, L. P.:Precision trace gas analysis by FT-IR spectroscopy 1. Simulta-neous analysis of CO2, CH4, N2O and CO in air, Anal. Chem.,72(1), 206–215, 2000.

Fu, D., Walker, K. A., Sung, K., Boone, C. D., Soucy, M.-A., andBernath, P. F.: The portable atmospheric research interferomet-ric spectrometer for the infrared, PARIS-IR, J. Quant. Spectrosc.Ra., 103, 362–370, 2007.

Galle, B., Bergquist, B., Ferm, M., Tornquist, K., Griffith, D. W. T.,Jensen, N. O., and Hansen, F.: Measurement of ammonia emis-sions from spreading of manure using gradient FTIR techniques,Atmos. Environ., 34, 4907–4915, 2000.

Gerlach, T. M., McGee, K. A., Sutton, A. J., and Elias, T.: Ratesof volcanic CO2 degassing from airborne determinations of SO2emission rates and plume CO2/SO2: Test study at Pu’u “O”ocone, Kilauea volcano, Hawaii, Geophys. Res. Lett., 25, 2675–2678, 1998.



Goode, J. G., Yokelson, R. J., Susott, R. A., and Ward, D. E.:Trace gas emissions from laboratory biomass fires measured byopen-path Fourier transform infrared spectroscopy: Fires in grassand surface fuels, J. Geophys. Res.-Atmos., 104(D17), 21237–21245, 1999.

Goode, J. G., Yokelson, R. J., Ward, D. E., Susott, R. A., Babbitt,R. E., Davies, A., and Min Hao, W.: Measurements of excessO3, CO2, CO, CH4, C2H4, C2H2, HCN, NO, NH3, NCOOH,CH3COOH, HCHO and CH3OH in 1997 Alaskan biomassburning plumes by airborne Fourier transform infrared spec-troscopy (AFTIR), J. Geophys. Res.-Atmos., 105(D17), 22147–22166, 2000.

Griffith, D. W. T.: Synthetic calibration and quantitative analysis ofgas-phase FTIR spectra, Appl. Spectrosc., 50, 59–70, 1996.

Griffith, D. W. T., Mankin, W. G., Coffey, M. T., Ward, D. E., andRiebau, A.: FTIR Remote Sensing of Biomass Burning Emis-sions of CO2, CO, CH4, CH2O, NO, NO2, NH3, and N2O,in: Global Biomass Burning, edited by: Levine, J. S., The MITPress, Cambridge, Massachusetts, 230–239, 1991.

Griffith, D. W. T., Leuning, R., Denmead, O. T., and Jamie, I. M.:Air-land exchanges of CO2, CH4 and N2O measured by FTIRspectrometry and micrometeorological techniques, Atmos. Env-iron., 36, 1833–1842, 2002.

Griffith, D. W. T., Esler, M. B., Paul Steele, L., and Reisinger, A.:Non-linear least squares: high precision quantitative analysis ofgas phase FTIR spectra, paper presented at 2nd Intl. Conferenceon Advanced Vibrational Spectroscopy, Nottingham, 2003.

Grutter, M.: Multi-Gas analysis of ambient air using FTIR spec-troscopy over Mexico City, Atmosfera, 16, 1–13, 2003.

Grutter, M., Flores, E., Basaldud, R., and Ruiz-Suarez, L. G.: Open-path FTIR spectroscopic studies of the trace gases over MexicoCity, Atmos. Ocean. Opt., 16(3), 232–236, 2003.

Haaland, D. M.: Multivariate calibration methods applied to quan-titative FT-IR analyses, in: Practical Fourier Transform In-frared Spectroscopy, Industrial and Laboratory Chemical Anal-ysis, edited by: Ferraro, J. R. and Krishnan, K., Academic, SanDiego, 395–468, 1990.

Hart, B. K., Berry, R. J., and Griffiths, P. R.: Effects of resolu-tion, spectral window, and background on multivariate calibra-tions used for open-path Fourier transform infrared spectrometry,Field Anal. Chem. Tech., 3(2), 117–130, 1999.

Hase, F., Demoulin, P., Sauval, A. J., Toon, G. C., Bernath, P. F.,Goldman, A., Hannigan, J. W., and Rinsland, C. P.: An empiricalline-by-line model for the infrared solar transmittance spectrumfrom 700 to 5000 cm−1, J. Quant. Spectrosc. Ra., 102, 450–463,2006.

Hong, D. W., Heo, G. S., Han, J. S., and Cho, S. Y.: Applicationof the open path FTIR with COL1SB to measurements of ozoneand VOCs in the urban area, Atmos. Environ., 38, 5567–5576,2004.

Horrocks, L. A., Burton, M. R., and Francis, P.: Stable gas plumecomposition measured by OP-FTIR spectroscopy at Masaya Vol-cano, Nicaragua, 1998–1999, Geophys. Res. Lett., 26(23), 3497–3500, 1999.

Horrocks, L. A., Oppenheimer, C., Burton, M. R., and Duffell, H.J.: Open-path Fourier transform infrared spectroscopy of SO2:An empirical error budget analysis, with implications for volcanomonitoring, J. Geophys. Res., 106(D21), 27647–27659, 2001.

Lamp, T., Radmacher, M., Weber, K., Gartner, A., Nitz, R., andBroker, G.: Calibration of an Open-Path FTIR spectrometer formethane, ethylene and carbon monoxide using a fixed 20 m multipass cell, Proc. SPIE, 3107, 126–136, 1997.

Levenburg, K.: A method for the solution of certain non-linearproblems in least squares, Quart. Appl. Math., 2, 164–168, 1944.

Marquardt, D.: An algorithm for least-squares estimation ofnonlinear parameters, SIAM J. Appl. Math., 11, 431–441,doi:10.1137/0111030, 1963.

Muller, U., Kurte, R., and Heise, H. M.: Investigation of photomet-ric errors in FTIR-spectra obtained in open-path monitoring, J.Mol. Struct., 482–483, 539–544, 1999.

Oppenheimer, C., Francis, P., Burton, M. R., Madejewsky, A. J. H.,and Boardman, L.: Remote measurement of volcanic gases byFourier transform infrared spectroscopy, Appl. Phys. B. LasersOpt., 67, 505–516, 1998.

Oppenheimer, C., Burton, M. R., Durieux, J., and Pyle, D. M.:Open-path Fourier transform spectroscopy of gas emissions fromOldoinyo Lengai volcano, Tanzania, Opt. Laser Eng., 37, 203–214, 2002.

Petropoulos, G., Wooster, M. J., Carlson, T. N., Kennedy, M. C.,and Scholze, M.: A global Bayesian sensitivity analysis of the 1dSimSphere soil-vegetation-atmospheric transfer (SVAT) modelusing Gaussian model emulation, Ecol. Model., 220(19), 2427–2440, doi:10.1016/j.ecolmodel.2009.06.006, 2009.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B.P.: Numerical Recipes, Cambridge University Press, Cambridge,1992.

Richter, D., Erdelyi, M., Curl, R. F., Tittel, F. K., Oppenheimer, C.,Duffell, H. J., and Burton, M.: Field measurements of volcanicgases using tunable diode laser based mid-infrared and Fouriertransform infrared spectrometers, Opt. Laser. Eng., 37, 171–186,2002.

Rigby, M., Toumi, R., Fisher, R., Lowry, D., and Nisbey, E. G.:First continuous measurements of CO2 mixing ratio in centralLondon using a compact diffusion probe, Atmos. Environ., 42,8943–8953, 2008.

Rinsland, C. P., Nicholas, B. J., Connor, B. J., Logan, J. A.,Pougatchev, N. S., Goldman, A., Murcray, F. J., Stephen,T. M., Pine, A. S., Zander, R., Mahieu, E., and Demoulin,P.: Northern and southern hemisphere ground-based infraredspectroscopic measurements of tropospheric carbon monox-ide and ethane, J. Geophy. Res., 103(D21), 28197–28218,doi:10.1029/98JD02515, 1998.

Rodgers, C. D.: Inverse Methods for Atmospheric Sounding: The-ory and Practice, World Scientific Publishing Co. Ltd., Singa-pore, 2000.

Rothman, L. S., Gordon, I. E., Barbe, A., Chris Benner, D.,Bernath, P. F., Birk, M., Boudon, V., Brown, L. R., Campar-gue, A., Champion, J.-P., Chance, K., Coudert, L. H., Dana,V., Devi, V. M., Fally, S., Flaud, J.-M., Gamache, R. R., Gold-man, A., Jacquemart, D., Kleiner, I., Lacome, N., Lafferty, W.J., Mandin, J.-Y., Massie, S. T., Mikhailenko, S. N., Miller, C.E., Moazzen-Ahmadi, N., Naumenko, O. V., Nikitin, A. V., Or-phal, J., Perevalov, V. I., Perrin, A., Predoi-Cross, A., Rinsland,C. P., Rotger, M.,Simeekova, M., Smith, M. A. H., Sung, K.,Tashkun, S. A., Tennyson, J., Toth, R. A., Vandaele, A. C., andVander Auwera, J.: TheHITRAN2008 molecular spectroscopicdatabase, J. Quant. Spectrosc. Ra., 110, 533–572, 2009.



Schafer, K., Haus, R., Heland, J., and Haak, A.: Measure-ments of atmospheric trace gases by emission and absorption-spectroscopy with FTIR, Phys. Chem. Chem. Phys., 99(3), 405–411, 1995.

Schafer, K., Jahn, C., Sturm, P., Lechner, B., and Bacher, M.: Air-craft emission measurements by remote sensing methodologiesat airports, Atmos. Environ., 37, 5261–5271, 2003.

Senten, C., De Maziere, M., Dils, B., Hermans, C., Kruglanski,M., Neefs, E., Scolas, F., Vandaele, A. C., Vanhaelewyn, G.,Vigouroux, C., Carleer, M., Coheur, P. F., Fally, S., Barret, B.,Baray, J. L., Delmas, R., Leveau, J., Metzger, J. M., Mahieu,E., Boone, C., Walker, K. A., Bernath, P. F., and Strong, K.:Technical Note: New ground-based FTIR measurements at Ilede La Reunion: observations, error analysis, and comparisonswith independent data, Atmos. Chem. Phys., 8, 3483–3508,doi:10.5194/acp-8-3483-2008, 2008.

Smith, B. C.: Fundamentals of Fourier Transform Infrared Spec-troscopy, CRC Press, New York, 224 pp., 1995.

von Bobrutzki, K., Braban, C. F., Famulari, D., Jones, S. K., Black-all, T., Smith, T. E. L., Blom, M., Coe, H., Gallagher, M., Gha-laieny, M., McGillen, M. R., Percival, C. J., Whitehead, J. D., El-lis, R., Murphy, J., Mohacsi, A., Pogany, A., Junninen, H., Ranta-nen, S., Sutton, M. A., and Nemitz, E.: Field inter-comparison ofeleven atmospheric ammonia measurement techniques, Atmos.Meas. Tech., 3, 91–112, doi:10.5194/amt-3-91-2010, 2010.

Yokelson, R. J., Susott, R., Ward, D. E., Reardon, J., and Griffith,D. W. T.: Emissions from smoldering combustion of biomassmeasured by open-path Fourier transform infrared spectroscopy,J. Geophys. Res., 102, 18865–18877, 1997.

Zhu, C. and Griffiths, P. R.: Extending the range of Beer’s lawin FT-IR spectrometry, Part I: Theoretical study of Norton-Beerapodization functions, Appl. Spectrosc., 52(11), 1403–1408,1998.


Absolute accuracy and sensitivity analysis of OP-FTIR ... · non-linear least squares ﬁtting...

Documents

Transcript of Absolute accuracy and sensitivity analysis of OP-FTIR ... · non-linear least squares ﬁtting...